Question 1

A polling agency wants to determine the size of a random sample needed to estimate theproportion of homeowners who keep a hand gun in their home for security. The estimate shouldhave margin of error no more than 2.5 percentage points at a 95% level of confidence. Choose themost conservative answer that is closest to your calculated number, rounding to the nearest wholeperson.

Accepted Answer

To find the sample size for a proportion with a given margin of error and confidence level, use the formula n = (Z^2 * p * (1-p)) / E^2. For the most conservative estimate, use p = 0.5. With a 95% confidence level, Z is approximately 1.96, and E is 0.025. Calculating gives n ≈ 1537, so the closest conservative choice is 1600.

Question 2

Which of the following statements is not true about a sampling distribution?

Accepted Answer

The answer of Which of the following statements is not...

Question 3

Use the following information to answer the question. In a recent poll of 1200 randomly selected adult office workers, 32%
said they had worn a Halloween costume to the office at least once.
-What is the margin of error, using a 95% confidence level, for estimating the true populationproportion of adult office workers who have worn a Halloween costume to the office at least once?(Round to the nearest thousandth)

Accepted Answer

The answer of Use the following information to answer the...

Question 4

Use the following information to answer the question. In a recent poll of 1200 randomly selected adult office workers, 32%said they had worn a Halloween costume to the office at least once.
-What is the standard error for the estimate of the proportion of all American adult office workers that have worn a Halloween costume to the office? Round to the nearest ten-thousandth.

Accepted Answer

The answer of Use the following information to answer the...

Question 5

According to a snack cracker manufacturer, a batch of butter crackers has a defect rate of 8%. Suppose a quality inspector randomly inspects 500 crackers. Complete the following statement: The Quality inspector should expect _{--------------------}defective crackers, give or take _{--------------------} Crackers.

Accepted Answer

The answer of According to a snack cracker manufacturer, a...

Question 6

There are four colors in a bag containing 500 plastic chips. It is known that 28% of the chips are green. On average, how many chips from a random sample of 50 (with replacement) would be
Expected to be green?

Accepted Answer

The expected number of green chips in a sample of 50 is calculated by multiplying the probability of a chip being green (28% or 0.28) by the sample size (50). Thus, 0.28 * 50 = 14.

Question 7

A random sample of 950 adult television viewers showed that 48% planned to watch sportingevent X. The margin of error is 4 percentage points with a 95% confidence. Does the confidenceinterval support the claim that the majority of adult television viewers plan to watch sporting eventX? Why?

Accepted Answer

The confidence interval is 44% to 52%, which means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 44% and 52%. Since the interval does not include 50%, we can conclude that the majority of adult television viewers plan to watch sporting event X.

Question 8

Use the following information to answer the question. A pescatarian is a person who eats fish and seafood but no otheranimal. An event planner does some research and finds that approximately 2.75% of the people in the area where a largeevent is to be held are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the localpopulation of about 150,000. -Suppose the event planner assumes that 4% of the guests will be pescatarian so he orders 10 pescatarian meals. What is the approximate probability that more than 4% of the guests are Pescatarian and that he will not have enough pescatarian meals? Round to the nearest thousandth.

Accepted Answer

The probability of more than 4% of the guests being pescatarian is 0.113. The probability of not having enough pescatarian meals is 0.001. The probability of both events happening is 0.113 * 0.001 = 0.000113.

Question 9

Use the following information to answer the question. A pescatarian is a person who eats fish and seafood but no other animal. An event planner does some research and finds that approximately 2.75% of the people in the area where a large event is to be held are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the local population of about 150,000.
-Suppose the event planner assumes that only 1.6% of the guests will be pescatarian so he orders 4pescatarian meals. What is the approximate probability that he will havetoo manypescatarianmeals? Round to the nearest thousandth.

Accepted Answer

The probability of having too many pescatarian meals is calculated using the binomial distribution with n = 250 and p = 0.0275. The probability of having 4 or fewer pescatarian guests is approximately 0.113.

Question 10

Use the following information to answer the question. In a recent poll of 1100 randomly selected home delivery truck drivers,26% said they had encountered an aggressive dog on the job at least once.
-What is the margin of error, using a 95% confidence level, for estimating the true populationproportion of home delivery truck drivers who have encountered an aggressive dog on the job atleast once? (Round to the nearest thousandth)

Accepted Answer

The margin of error (ME) for a proportion is calculated using the formula: ME = Z * sqrt[(p(1-p))/n], where Z is the Z-score for a 95% confidence level (approximately 1.96), p is the sample proportion (0.26), and n is the sample size (1100). Calculating this gives approximately 0.026.

Question 11

Researchers are interested in learning more about the age of women when they marry for the first time so they survey 500 married or divorced women and ask them how old they were when theyFirst married. The collection of the ages of the 500 women when they first Married is a _{--------------------}.

Accepted Answer

The collection of ages from the 500 women surveyed is a sample, as it represents a subset of the larger population of all married or divorced women.

Question 12

If it is being used to make inferences about a population, a good statistic (or estimator) should

Accepted Answer

A good statistic should be accurate and precise in order to provide an unbiased representation of the population being studied. Showing correlation is not necessarily a requirement for a good statistic, and being derived from population data is not always possible or necessary (for example, a sample statistic may be used to make inferences about a different population).

Question 13

Suppose that in a recent poll of 1200 adults Suppose that in a recent poll of 1200 adults between the ages of 35 and 45, 38% surveyed said theyhave thought about getting elective plastic surgery. Find the 95% confidence interval for theproportion of adults ages 35 to 45 who have thought about getting elective plastic surgery thenchoose the correct interpretation. (Round to the nearest tenth of a percent)

Accepted Answer

The 95% confidence interval for the proportion is calculated using the formula: p̂ ± Z*(√(p̂(1-p̂)/n)), where p̂ = 0.38, Z = 1.96 for 95% confidence, and n = 1200. This results in an interval of approximately 35.2% to 40.7%.

Question 14

Fill in the blank to complete the statement.
-Suppose that the age of all the U. S. vice presidents when they took office was recorded. The collection of the ages of all the U. S. vice presidents when they took office is a .

Accepted Answer

The collection of ages of all U.S. vice presidents when they took office represents the entire group of interest, making it a population.

Question 15

Fill in the blank to complete the statement.
-Researchers are interested in learning more about the age of men when they marry for the first time so they survey 500 married or divorced men and ask them how old they were when they first
Married. The mean of age of the 500 men when they married for the first time would be a

Accepted Answer

The mean age of the 500 men surveyed is a statistic because it is a numerical summary calculated from a sample, not the entire population.

Question 16

Suppose that Illinois lawmakers survey 130 randomly selected registered voters to see if they favorcharging a deposit on aluminum cans to encourage recycling. The lawmakers believe thepopulation proportion in favor of changing the law is 93% (based on historical data and previousvotes). Which of the following conditions for the Central Limit theorem arenotmet?

Accepted Answer

The condition for the Central Limit Theorem requires that both np and n(1-p) be greater than 5. Here, n(1-p) = 130 * 0.07 = 9.1, which is greater than 5, so the condition is met.

Question 17

Use the following information to answer the question. In a recent poll of 1100 randomly selected home delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once.
-What is the standard error for the estimate of the proportion of all home delivery truck drivers who have encountered an aggressive dog on the job at least once? Round to the nearest ten-thousandth.

Accepted Answer

To calculate the standard error, we use the formula:
SE = sqrt[(p*(1-p))/n]
Where p is the proportion of home delivery truck drivers who have encountered an aggressive dog on the job at least once, and n is the sample size.
Plugging in the values, we get:
SE = sqrt[(0.26*(1-0.26))/1100]
SE ≈ 0.0132 (rounded to the nearest ten-thousandth)
Therefore, the correct answer is C, 0.0132.

Question 18

Use the following information to answer the question. A pollotarian is a person who eats poultry but no red meat. Awedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is tobe held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population ofabout 200,000.
-Suppose the wedding planner assumes that only 3% of the guests will be pollotarian so she orders 9pollotarian meals. What is the approximate probability that she will havetoo manypollotarianmeals? Round to the nearest thousandth.

Accepted Answer

The probability that more than 9 out of 300 guests are pollotarian can be calculated using the binomial distribution with n=300 and p=0.035. The probability of having 9 or fewer pollotarian guests is approximately 0.681, so the probability of having more than 9 is 1 - 0.681 = 0.319.

Question 19

Max is interested in whether there is community interest in having local musicians perform musicin the park in the evenings during the summer. Max goes to the park for several evenings in a rowand asks people visiting the park whether they would like to hear music in the evening. Out of the200 people he surveys, 58% respond favorably. This scenario is describing what type of samplingbias?

Accepted Answer

Max's method of surveying people who are already at the park may lead to voluntary response bias, as those present might have a particular interest in park activities, skewing the results.

Question 20

Report the 95% confidence interval for the proportion of all adult office workers who have worn a Halloween costume to the office at least once. (Round final calculations to the nearest tenth of a
Percent)

Accepted Answer

The answer of Report the 95% confidence interval for the...

Quiz 7: Survey Sampling and Inference

Which of the following statements is not true about a sampling distribution?

There are four colors in a bag containing 500 plastic chips. It is known that 28% of the chips are green. On average, how many chips from a random sample of 50 (with replacement) would be Expected to be green?

A random sample of 950 adult television viewers showed that 48% planned to watch sportingevent X. The margin of error is 4 percentage points with a 95% confidence. Does the confidenceinterval support the claim that the majority of adult television viewers plan to watch sporting eventX? Why?

Researchers are interested in learning more about the age of women when they marry for the first time so they survey 500 married or divorced women and ask them how old they were when theyFirst married. The collection of the ages of the 500 women when they first Married is a _{--------------------}.

If it is being used to make inferences about a population, a good statistic (or estimator) should

Fill in the blank to complete the statement. -Suppose that the age of all the U. S. vice presidents when they took office was recorded. The collection of the ages of all the U. S. vice presidents when they took office is a .

Report the 95% confidence interval for the proportion of all adult office workers who have worn a Halloween costume to the office at least once. (Round final calculations to the nearest tenth of a Percent)

Quiz 7: Survey Sampling and Inference

Which of the following statements is not true about a sampling distribution?

There are four colors in a bag containing 500 plastic chips. It is known that 28% of the chips are green. On average, how many chips from a random sample of 50 (with replacement) would be Expected to be green?

A random sample of 950 adult television viewers showed that 48% planned to watch sportingevent X. The margin of error is 4 percentage points with a 95% confidence. Does the confidenceinterval support the claim that the majority of adult television viewers plan to watch sporting eventX? Why?

Researchers are interested in learning more about the age of women when they marry for the first time so they survey 500 married or divorced women and ask them how old they were when theyFirst married. The collection of the ages of the 500 women when they first Married is a --------------------.

If it is being used to make inferences about a population, a good statistic (or estimator) should

Fill in the blank to complete the statement. -Suppose that the age of all the U. S. vice presidents when they took office was recorded. The collection of the ages of all the U. S. vice presidents when they took office is a .

Report the 95% confidence interval for the proportion of all adult office workers who have worn a Halloween costume to the office at least once. (Round final calculations to the nearest tenth of a Percent)

Researchers are interested in learning more about the age of women when they marry for the first time so they survey 500 married or divorced women and ask them how old they were when theyFirst married. The collection of the ages of the 500 women when they first Married is a _{--------------------}.